MinT - Best Known (197−53, 197, s)-Nets in Base 3

Best Known (197−53, 197, s)-Nets in Base 3

(197−53, 197, 288)-Net over F₃ — Constructive and digital

Digital (144, 197, 288)-net over F₃, using

t-expansion [i] based on digital (143, 197, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 66, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(197−53, 197, 635)-Net over F₃ — Digital

Digital (144, 197, 635)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−53, 197, 20820)-Net in Base 3 — Upper bound on s

There is no (144, 197, 20821)-net in base 3, because

1 times m-reduction [i] would yield (144, 196, 20821)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3281 071558 087770 833963 913813 080579 428450 425381 669590 967081 198646 126585 609717 925154 071935 346001 > 3¹⁹⁶ [i]